Learning optimal orders of the underlying Euclidean norm in total variation image denoising

Pan Liu; Carola-Bibiane Schönlieb

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arXiv · 1903.11953

Learning optimal orders of the underlying Euclidean norm in total variation image denoising

Pan Liu·Carola-Bibiane Schönlieb

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Abstract

A novel class of semi-norms, generalising the notion of the isotropic total variation $TV_{2}$ and the an-isotropic total variation $TV_{1}$ is introduced. A supervised learning method via bilevel optimisation is proposed for the computation of optimal parameters for this class of regularizers. Existence of solutions to the bilevel optimisation approach is proven. Moreover, a finite-dimensional approximation scheme for the bilevel optimisation approach is introduced that can numerically compute a global optimizer to any given accuracy.

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Pan Liu, Carola-Bibiane Schönlieb. 2019-03-28. Learning optimal orders of the underlying Euclidean norm in total variation image denoising. https://arxiv.org/abs/1903.11953

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